Evaluate the integral using the integration by parts technique. $(6$ points$)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}3x{e}^{x}dx$

Determine if the improper integral converges or diverges. If it converges, state the exact value. To receive full credit your answer must include the correct limit notation. $(9$ points$)$

${\displaystyle \underset{1}{\overset{}{}}}\frac{7}{x^2}dx$